Abstract
Near-field radiative transfer between two objects can be computed using Rytov's theory of fluctuational electrodynamics in which the strength of electromagnetic sources is related to temperature through the fluctuation-dissipation theorem, and the resultant energy transfer is described using the dyadic Green's function of the vector Helmholtz equation. When the two objects are spheres, the dyadic Green's function can be expanded in a series of vector spherical waves. Based on comparison with the convergence criterion for the case of radiative transfer between two parallel surfaces, we derive a relation for the number of vector spherical waves required for convergence in the case of radiative transfer between two spheres. We show that when electromagnetic surface waves are active at a frequency the number of vector spherical waves required for convergence is proportional to Rmax/d when d/Rmax → 0, where Rmax is the radius of the larger sphere, and d is the smallest gap between the two spheres. This criterion for convergence applies equally well to other near-field electromagnetic scattering problems.
Highlights
Electromagnetic scattering from a sphere is a well studied topic since the seminal work of Mie [1]
Let us consider the problem of scattering of an electromagnetic plane wave from a spherical particle in a homogeneous medium to give a brief introduction to the vector spherical wave expansion method that is used in this work
We conclude that Eq (13) is expected to hold true even in the limiting case of R1 → 0, which implies that to determine the scattered field due to excitation by a dipole current source at a distance z( λ ) from the surface of a sphere of radius R, Nconv scales as R/z. This can be used as a criterion for the convergence of the number of terms to be retained in the summation over l while calculating quantities such as local density of states (LDOS) near the surface of a sphere, like in [52]
Summary
Electromagnetic scattering from a sphere is a well studied topic since the seminal work of Mie [1]. The near-field contribution to the thermal radiative transfer between polar dielectric surfaces (like SiO2, SiC, etc) separated by a vacuum gap is dominated by tunneling of electromagnetic surface modes [23,24,25]. These modes are characterized by the presence of large energy density at the interface between the dielectric medium and vacuum and decay rapidly with distance from the surface [19]. With parallel surfaces, it has not been possible to explore near-field effects at sub-micron gaps For this reason, numerical models of near-field radiative transfer between spherical surfaces are important. We will demonstrate the importance of a new convergence criteria by calculating the enhanced thermal radiative transfer between two silica spheres due to the tunneling of electromagnetic surface modes
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